{"id":48924,"date":"2016-09-11T15:11:08","date_gmt":"2016-09-11T18:11:08","guid":{"rendered":"https:\/\/www.estrategiaconcursos.com.br\/blog\/?p=48924"},"modified":"2018-09-21T17:55:02","modified_gmt":"2018-09-21T20:55:02","slug":"matematica-financeira-tcepr-gabarito-extraoficial-e-prova-resolvida","status":"publish","type":"post","link":"https:\/\/www.estrategiaconcursos.com.br\/blog\/matematica-financeira-tcepr-gabarito-extraoficial-e-prova-resolvida\/","title":{"rendered":"Matem\u00e1tica Financeira TCE\/PR &#8211; gabarito extraoficial e prova resolvida"},"content":{"rendered":"<p>Caros alunos,<\/p>\n<p style=\"text-align: justify;\">Vejam abaixo a resolu\u00e7\u00e3o das quest\u00f5es de Matem\u00e1tica Financeira da prova de Analista do TCE\/PR 2016, da banca CESPE, com o meu gabarito extra oficial. Utilizei o caderno de provas da \u00c1rea Administra\u00e7\u00e3o, ok?<\/p>\n<p style=\"text-align: justify;\"><em><strong>***Atualiza\u00e7\u00e3o: hoje, 13\/09, foi publicado o gabarito preliminar do Cespe. Entendo que n\u00e3o h\u00e1 recurso, pois todos os gabaritos bateram com a minha resolu\u00e7\u00e3o extra oficial***<\/strong><\/em><\/p>\n<p style=\"text-align: justify;\"><strong>CESPE &#8211; TCE\/PR &#8211; 2016) Um empr\u00e9stimo de R$240.000&#8230;<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>RESOLU\u00c7\u00c3O:<\/strong><\/p>\n<p style=\"text-align: justify;\">No sistema de amortiza\u00e7\u00e3o constante, a amortiza\u00e7\u00e3o mensal \u00e9:<\/p>\n<p style=\"text-align: justify;\">A = VP\/n = 240.000 \/ 12 = 20.000 reais<\/p>\n<p style=\"text-align: justify;\">A taxa de juros nominal de 12%aa corresponde \u00e0 taxa efetiva de 1%am (afinal o financiamento \u00e9 mensal). Se fosse usado o SAC, no in\u00edcio do terceiro per\u00edodo j\u00e1 ter\u00edamos amortizado 2 cotas de 20.000 cada, sobrando um saldo devedor de 200.000 reais. Os juros do terceiro per\u00edodo seriam:<\/p>\n<p style=\"text-align: justify;\">J3 = 1% x 200.000 = 2.000 reais<\/p>\n<p style=\"text-align: justify;\">Portanto, a presta\u00e7\u00e3o no sistema SAC seria P = A + J = 20.000 + 2.000 = 22.000 reais.<\/p>\n<p style=\"text-align: justify;\">No sistema misto, a presta\u00e7\u00e3o \u00e9 a m\u00e9dia entre SAC e Price:<\/p>\n<p style=\"text-align: justify;\">Presta\u00e7\u00e3o SAM = (22.000 + 21.324) \/ 2 = 21.662 reais<\/p>\n<p style=\"text-align: justify;\"><strong>Resposta: B (R$21.662)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>CESPE &#8211; TCE\/PR &#8211; 2016) Ao estudar uma proposta de neg\u00f3cio&#8230;\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>RESOLU\u00c7\u00c3O:<\/strong><\/p>\n<p style=\"text-align: justify;\">O valor presente dos retornos futuros \u00e9 dado por:<\/p>\n<p style=\"text-align: justify;\">VP = 55.000 \/ (1+10%)^1 + 65.000\/(1+10%)^2<\/p>\n<p style=\"text-align: justify;\">VP = 55.000\/1,1 + 65.000\/1,21<\/p>\n<p style=\"text-align: justify;\">Este valor presente deve ser igual \u00e0quele que seria obtido com dois recebimentos iguais, cada um de valor &#8220;P&#8221;. Neste caso, o c\u00e1lculo seria:<\/p>\n<p style=\"text-align: justify;\">VP = P\/1,1 + P\/1,21<\/p>\n<p style=\"text-align: justify;\">Igualando esses valores presentes,<\/p>\n<p style=\"text-align: justify;\">55.000\/1,1 + 65.500\/1,21 =\u00a0P\/1,1 + P\/1,21<\/p>\n<p style=\"text-align: justify;\">Multiplicando todos os termos por 1,21, que \u00e9 o mesmo que 1,1&#215;1,1, ficamos com:<\/p>\n<p style=\"text-align: justify;\">55.000&#215;1,1 + 65.500 = Px1,1 + P<\/p>\n<p style=\"text-align: justify;\">60.500 + 65.500 = 2,1P<\/p>\n<p style=\"text-align: justify;\">P = 126.000 \/ 2,1<\/p>\n<p style=\"text-align: justify;\">P = 60.000 reais<\/p>\n<p style=\"text-align: justify;\"><strong>Resposta: D (R$60.000)<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>CESPE &#8211; TCE\/PR &#8211; 2016) Um investidor possui as propostas A e B&#8230;\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>RESOLU\u00c7\u00c3O:<\/strong><\/p>\n<p style=\"text-align: justify;\">No investimento A temos taxa nominal de 14,4%aa com capitaliza\u00e7\u00e3o mensal, o que nos d\u00e1 uma taxa efetiva de 14,4% \/ 12 = 1,2%am. Em um ano (12 meses), teremos:<\/p>\n<p style=\"text-align: justify;\">M = C x (1+j)^t<\/p>\n<p style=\"text-align: justify;\">M = 10.000x(1+1,2%)^12<\/p>\n<p style=\"text-align: justify;\">M = 10.000&#215;1,012^12<\/p>\n<p style=\"text-align: justify;\">M =10.000&#215;1,1538<\/p>\n<p style=\"text-align: justify;\">M = 11.538 reais<\/p>\n<p style=\"text-align: justify;\">Os juros do investimento A s\u00e3o de J = 11.538 &#8211; 10.000 = 1.538 reais.<\/p>\n<p style=\"text-align: justify;\">No investimento B temos taxa nominal de 15%aa com capitaliza\u00e7\u00e3o bimestral, o que nos d\u00e1 uma taxa efetiva de 15% \/ 6 = 2,5% ao bimestre. Em um ano (6 bimestres), temos:<\/p>\n<p style=\"text-align: justify;\">M = 10.000x(1+2,5%)^6<\/p>\n<p style=\"text-align: justify;\">M = 10.000&#215;1,025^6<\/p>\n<p style=\"text-align: justify;\">M = 10.000&#215;1,1596<\/p>\n<p style=\"text-align: justify;\">M = 11.596 reais<\/p>\n<p style=\"text-align: justify;\">Os juros do investimento B s\u00e3o de J = 11.596 &#8211; 10.000 = 1.596 reais. Temos essa informa\u00e7\u00e3o na alternativa B.<\/p>\n<p style=\"text-align: justify;\">Veja ainda que a taxa efetiva em A \u00e9 15,38%aa, e em B \u00e9 de 15,96%aa (de modo que a taxa efetiva em B \u00e9 maior, o que torna errada a alternativa a da quest\u00e3o).<\/p>\n<p style=\"text-align: justify;\"><strong>Resposta: B (O investimento B pagar\u00e1 um retorno de R$1.596).<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>CESPE &#8211; TCE\/PR &#8211; 2016) Carla, que planeja viajar daqui&#8230;<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>RESOLU\u00c7\u00c3O:<\/strong><\/p>\n<p style=\"text-align: justify;\">Vamos calcular o valor futuro de n = 6 dep\u00f3sitos mensais de valor P = 2.000 reais cada, considerando a taxa j = 1% ao m\u00eas. Para isso, o fator de acumula\u00e7\u00e3o de capital \u00e9:<\/p>\n<p style=\"text-align: justify;\">s(n,j) = [(1+j)^n &#8211; 1] \/ j<\/p>\n<p style=\"text-align: justify;\">s(6,1%) = [(1,01)^6-1]\/0,01 = [1,0615-1] \/ 0,01 = 6,15<\/p>\n<p style=\"text-align: justify;\">Portanto, o valor futuro \u00e9:<\/p>\n<p style=\"text-align: justify;\">VF = s(n,j) x P<\/p>\n<p style=\"text-align: justify;\">VF = 6,15 x 2.000<\/p>\n<p style=\"text-align: justify;\">VF = 12.300 reais<\/p>\n<p style=\"text-align: justify;\">Portanto, logo ap\u00f3s o sexto dep\u00f3sito Carla ter\u00e1 12.300 reais. Um m\u00eas ap\u00f3s esta data ela come\u00e7ar\u00e1 a resgatar n = 6 saques de valor &#8220;P&#8221;. Esses saques devem ter o mesmo valor presente do montante acumulado (12.300), considerando a taxa de 1%am novamente. Assim,<\/p>\n<p style=\"text-align: justify;\">VP = a(n,j) x P<\/p>\n<p style=\"text-align: justify;\">12.300 = a(6,1%) x P<\/p>\n<p style=\"text-align: justify;\">a(n,j) = [(1+j)^n-1] \/ [j.(1+j)^n]<\/p>\n<p style=\"text-align: justify;\">a(6,1%) = [(1,01)^6-1] \/ [0,01.(1,01)^6]<\/p>\n<p style=\"text-align: justify;\">a(6,1%) = [1,0615-1] \/ [0,01.1,0615]<\/p>\n<p style=\"text-align: justify;\">a(6,1%) = 0,0615 \/ 0,010615<\/p>\n<p style=\"text-align: justify;\">a(6,1%) = 615 \/ 106,15<\/p>\n<p style=\"text-align: justify;\">Assim,<\/p>\n<p style=\"text-align: justify;\">12.300 = a(6,1%) x P<\/p>\n<p style=\"text-align: justify;\">12.300 =\u00a0(615\/106,15) x P<\/p>\n<p style=\"text-align: justify;\">P = 106,15 x 12.300 \/ 615<\/p>\n<p style=\"text-align: justify;\">P = 106,15 x 20<\/p>\n<p style=\"text-align: justify;\">P = 212,30 x 10<\/p>\n<p style=\"text-align: justify;\">P = 2123,0 reais<\/p>\n<p style=\"text-align: justify;\"><strong>Resposta: E<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Caros alunos, Vejam abaixo a resolu\u00e7\u00e3o das quest\u00f5es de Matem\u00e1tica Financeira da prova de Analista do TCE\/PR 2016, da banca CESPE, com o meu gabarito extra oficial. Utilizei o caderno de provas da \u00c1rea Administra\u00e7\u00e3o, ok? ***Atualiza\u00e7\u00e3o: hoje, 13\/09, foi publicado o gabarito preliminar do Cespe. Entendo que n\u00e3o h\u00e1 recurso, pois todos os gabaritos [&hellip;]<\/p>\n","protected":false},"author":48,"featured_media":43262,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"post_tipo":"article","footnotes":""},"categories":[],"tags":[1847],"tax_estado":[],"class_list":["post-48924","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","tag-concurso-tce-pr"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.2 (Yoast SEO v27.2) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Matem\u00e1tica Financeira TCE\/PR - gabarito extraoficial e prova resolvida<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.estrategiaconcursos.com.br\/blog\/matematica-financeira-tcepr-gabarito-extraoficial-e-prova-resolvida\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Matem\u00e1tica Financeira TCE\/PR - gabarito extraoficial e prova resolvida\" \/>\n<meta property=\"og:description\" content=\"Caros alunos, Vejam abaixo a resolu\u00e7\u00e3o das quest\u00f5es de Matem\u00e1tica Financeira da prova de Analista do TCE\/PR 2016, da banca CESPE, com o meu gabarito extra oficial. Utilizei o caderno de provas da \u00c1rea Administra\u00e7\u00e3o, ok? ***Atualiza\u00e7\u00e3o: hoje, 13\/09, foi publicado o gabarito preliminar do Cespe. 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Utilizei o caderno de provas da \u00c1rea Administra\u00e7\u00e3o, ok? ***Atualiza\u00e7\u00e3o: hoje, 13\/09, foi publicado o gabarito preliminar do Cespe. 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